Vertical localization, particularly floor separation, remains a major challenge in indoor positioning systems operating in GPS-denied multistory environments. This paper proposes a fully data-driven, graph-based framework for blind floor separation using only Wi-Fi fingerprint trajectories, without requiring prior building information or knowledge of the number of floors. In the proposed method, Wi-Fi fingerprints are represented as nodes in a trajectory graph, where edges capture both signal similarity and sequential movement context. Structural node embeddings are learned via Node2Vec, and floor-level partitions are obtained using K-Means clustering with automatic cluster number estimation. The framework is evaluated on multiple publicly available datasets, including a newly released Huawei University Challenge 2021 dataset and a restructured version of the UJIIndoorLoc benchmark. Experimental results demonstrate that the proposed approach effectively captures the intrinsic vertical structure of multistory buildings using only received signal strength data. By eliminating dependence on building-specific metadata, the proposed method provides a scalable and practical solution for vertical localization in indoor environments.